EP2879341B1 - Channel-estimation method for FBMC telecommunication system - Google Patents

Description

TECHNICAL AREA

The present invention generally relates to the field of telecommunication systems using filter bank multi-carrier modulation, also referred to as FBMC (Filter Bank Multi-Carrier) systems.

PRIOR ART

Telecommunication systems using multi-carrier modulation are well known in the state of the art. The principle of such modulation consists in dividing the transmission band into a plurality of frequency sub-channels associated with sub-carriers and in modulating each of these sub-carriers by the data to be transmitted.

The most widespread multi-carrier modulation is undoubtedly the OFDM modulation (Orthogonal Frequency Division Multiplexing). This is implemented in wireless local area networks WLAN, WiFi, in wireless broadband internet access (WiMAX), digital broadcasting systems (DVB-T, ISDB-T, DAB), asymmetric digital (xDSL), the fourth generation of cellular telephony (LTE), etc.

In an OFDM transmission system, each block of OFDM symbols is preceded by a guard interval or else by a cyclic prefix, longer than the time spread of the impulse response of the channel, so as to eliminate the interference. intersymbol. The insertion of a guard interval or a prefix however leads to a loss of spectral efficiency. Finally, the spectral occupancy of an OFDM signal being noticeably greater than the band of sub-carriers that it uses in Due to the spreading of the secondary lobes, OFDM modulation is not an optimal solution for applications requiring high out-of-band rejection ratios.

A filter bank modulation or FBMC (Filter Bank Multi Carrier) can be used as an alternative to OFDM modulation.

A comparison between FBMC systems and OFDM systems is presented in the article by B. Farhang-Bouroujeny entitled “OFDM versus filter bank multicarrier” published in IEEE Signal Processing Magazine, pp. 91-112, March 2011 .

The principle of FBMC modulation is based on a synthesis by bank of filters on transmission and an analysis by bank of filters on reception.

The Fig. 1 schematically represents the structure of a first FBMC transmission/reception system known from the state of the art.

This structure has been described in detail in the article by B. Hirosaki entitled “An orthogonally multiplexed QAM system using the discrete Fourier transform” published in IEEE Trans on Comm., vol. 29 No. 7, p. 982-989, July 1981 , as well as in the article by P. Siohan et al. entitled "Analysis and design of OFDM/OQAM systems based on filterbank theory" published in IEEE Trans. on signal processing, vol. 50, No 5, pp. 1170-1183, May 2002 .

At the transmitter level, the QAM modulation symbols to be transmitted with a rate Nf where f =1/ T are grouped into blocks of size N, x ₀ [ n ],..., x _{N -1} [ n ] , where _n is the time index of the block. Each block of N symbols is supplied in parallel to N input channels of a preprocessing module 110, referred to as OQAM (Offset QAM) preprocessing. This pre-processing module performs an OQAM-type data modulation, that is to say temporally demultiplexes the real part and the imaginary part of x _k [ n ] with a rate of 2 f .

The samples thus obtained are supplied in the form of blocks of size N to a bank of synthesis filters 120, consisting of an IFFT (inverse fast Fourier transform) module of size N, 130, of a plurality N of polyphase filters 133, of a plurality of over-samplers 135, of factor M = N /2, at the output of the various filters polyphase, and finally a plurality of delays, 137, arranged in parallel and varying from 0 to N - 1 sampling periods. Each of the N processing channels corresponds to a sub-channel.

The outputs of the polyphase, oversampled and delayed filters are summed by adder 139 before transmission on channel 150.

Polyphase filters are frequency-translated versions of k / MT of a prototype filter whose impulse response is of duration KT , i.e. the output of one polyphase filter temporally overlaps the output of the adjacent polyphase filter by M samples. As a result, a polyphase filter output temporally overlaps K other polyphase filter outputs. The coefficient K is therefore called the overlapping factor .

On the receiver side, the received signal is sampled with a rate Nf . The samples are supplied in the form of blocks of size N to an analysis filter bank, 160, comprising a plurality of delays, 163, arranged in parallel and varying from 0 to N -1 sampling periods, in the order inverse of the delays 137. The streams of samples coming from the various delays are then decimated by a factor M = N /2 by the decimators 165 then filtered by the analysis filters 167. The analysis filters have a combined impulse response and reversed in time with respect to the corresponding synthesis filter. Since the prototype filter is real-valued and time-reversed, an analysis filter can be shown to have the same impulse response as the corresponding synthesis filter. The combination of a synthesis filter with the corresponding analysis filter (product of the transfer functions) gives a Nyquist filter.

The symbols at the output of the synthesis filters then undergo an FFT (fast Fourier transform) of size N at 170, the various frequency components of the FFT then being supplied to the post-processing module 180 carrying out an inverse processing from that of pretreatment 110.

The synthesis/analysis filtering being carried out in the time domain, respectively at the output of the IFFT module and at the input of the FFT module, the FBMC system illustrated in Fig. 1 will be said to be implemented in the time domain.

The FBMC system is capable of representation in the frequency domain as described in the document of M. Bellanger et al. entitled “FBMC physical layer: a primer” available on the website www.ict-phydyas.org .

An implementation of the FBMC system in the frequency domain is shown in Fig. 2 .

We find in Fig. 2 the pre-processing module 210 performing an OQAM modulation of the data to be transmitted.

Each of the data is then spread in frequency over an interval of 2K-1 adjacent sub-carriers centered on a sub-channel sub-carrier, each data being weighted by the (real) value taken by the transfer function of the synthesis filter at the corresponding frequency. In other words, each OQAM symbol d _i [ n ] is spread over 2 K -1 adjacent sub-carriers to give: $${\stackrel{⌣}{}}_{I,k}\left[\mathrm{not}\right]={}_I\left[\mathrm{not}\right]G_k,k=-K+1,\dots ,0,..K-1$$

The frequency spreading and filtering module by the prototype filter is designated by 220. It will be understood that this operation is equivalent to that of the filtering by the synthesis filters 133 in the temporal implementation.

Data of the same parity i and i + 2 are spectrally separated and those of opposite parities i and i + 1 overlap as shown in Fig. 3A . However, this overlap does not generate interference since two data items of opposite parity are necessarily located respectively on the real axis and the imaginary axis. For example, in Fig. 3A , the data d _i [ n ] and d _{i +2} [ n ] are real values (represented by solid lines) while the data d _{i +1} [ n ] is an imaginary value (represented by dotted lines).

The frequency-spread and filtered data is then subjected to an IFFT of size KN at 230. Note that the size of the IFFT is extended by a factor K by compared to that of the Fig. 1 , the filtering by the synthesis filters being found here performed upstream of the IFFT, in the frequency domain.

The outputs of the IFFT are then combined in the combiner 240 as shown in Fig. 4 . The set of samples at the output of the IFFT represents an FBMC symbol in the time domain, it being understood that the real part and the imaginary part of this symbol are shifted by T /2. The FBMC symbols each having a duration KT and succeeding each other at the rate f =1/ T , an FBMC symbol is combined in the module 240 with the K /2 preceding FBMC symbols and K /2 following FBMC symbols. For this reason K is also called overlapping factor .

It should be noted that the combination operation at 240 is equivalent to that occurring within the synthesis filters of the Fig. 1 .

The signal thus obtained is then translated into the RF band.

After transmission on channel 250, the signal received, demodulated in baseband, is sampled by the receiver at the rate Nf.

A sliding FFT (the window of the sliding FFT of KT between two FFT calculations) of size KN is performed in the FFT module, 260, on blocks of consecutive KN samples.

, k = -K + 1,..., 0,..K - 1 correspondant aux 2K-1 fréquences (i-1)K + 1,...iK ,... (i+1)K-1 de la FFT sont multipliés par les valeurs de la fonction de transfert du filtre d'analyse (translatée en fréquence de celle du filtre prototype) aux fréquences en question et les résultats obtenus sont sommés, soit : $$d_i^r\left[n\right]={\displaystyle \sum _{k=-K+1}^{K-1}{G}_k{\stackrel{⌣}{d}}_{i,k}^r\left[n\right]}$$

The outputs of the FFT are then subjected to spectral filtering and despreading in module 270. The despreading operation takes place in the frequency domain as shown in Fig. 3B . Specifically the samples ${\stackrel{⌣}{}}_{I,k}^r\left[\mathrm{not}\right]$

, k = - K + 1,..., 0,.. K - 1 corresponding to the 2 K -1 frequencies ( i -1) K + 1,... iK ,... ( i +1) K - 1 of the FFT are multiplied by the values of the transfer function of the analysis filter (translated in frequency from that of the prototype filter) at the frequencies in question and the results obtained are summed, i.e.: $${}_I^r\left[\mathrm{not}\right]={\displaystyle \sum _{k=-K+1}^{K-1}{G}_k{\stackrel{⌣}{}}_{I,k}^r\left[\mathrm{not}\right]}$$

et $d_{i+2}^r\left[n\right]$

font appel à des blocs d'échantillons disjoints alors que ceux de deux rangs consécutifs, de parités inverses, se chevauchent. Ainsi, l'obtention de la donnée $d_{i+1}^r\left[n\right]$

fait appel aux échantillons ${\stackrel{⌣}{d}}_{i,k}^r\left[n\right]$

, k = 1,.., K -1 ainsi qu'aux échantillons ${\stackrel{⌣}{d}}_{i+2,k}^r\left[n\right]$

, k = -K + 1,...,1 .Note that, as in Fig. 3A , obtaining data having ranks of same parity, for example ${}_I^r\left[\mathrm{not}\right]$

and ${}_{I+2}^r\left[\mathrm{not}\right]$

use blocks of disjoint samples whereas those of two consecutive ranks, of inverse parities, overlap. Thus, obtaining the data ${}_{I+1}^r\left[\mathrm{not}\right]$

calls for samples ${\stackrel{⌣}{}}_{I,k}^r\left[\mathrm{not}\right]$

, k = 1,.., K -1 as well as to the samples ${\stackrel{⌣}{}}_{I+2,k}^r\left[\mathrm{not}\right]$

, k = -K + 1,...,1 .

The despreading of real data is represented by continuous lines while that of imaginary data is represented by dotted lines.

It is also important to note that the filtering by the analysis filters is here carried out in the frequency domain, downstream of the FFT, contrary to the embodiment of the Fig. 1 .

ainsi obtenues sont ensuite fournies à un module de post-traitement 280, effectuant le traitement inverse de celui du module 210, autrement dit une démodulation OQAM.Data ${}_I^r\left[\mathrm{not}\right]$

thus obtained are then supplied to a post-processing module 280, performing the inverse processing to that of the module 210, in other words an OQAM demodulation.

One of the problems to be solved in FBMC systems is to perform the estimation of the transmission channel. This channel estimate is necessary in order to be able to equalize the signal in reception and restore the transmitted message.

In OFDM systems, a so-called one-coefficient equalization is generally performed per sub-carrier, at least as long as the time spread of the channel remains less than the duration of the guard interval (or of the prefix).

The Fig. 3 illustrates a known equalization scheme for an OFDM receiver.

The received signal is subjected to an FFT in the module 310 after baseband demodulation and analog-digital conversion.

A channel estimator 320 estimates the (complex) attenuation coefficients for each sub-carrier of the OFDM multiplex and transmits these coefficients to an equalization module operating on each of the sub-carriers. The equalization module 330 can perform an equalization by subcarrier of the ZF ( Zero Forcing ) type or of the MMSE ( Minimum Mean Square Error ) type in a manner known per se.

Channel estimation in an OFDM system typically requires inserting pilot symbols, that is to say symbols known to the receiver, in a frame of OFDM symbols transmitted by the transmitter. These pilot symbols are distributed on different sub-carriers of the OFDM multiplex. The channel estimator is then able to determine the (complex) attenuation coefficient of the channel for each of the sub-carriers carrying a pilot symbol and, if necessary, to deduce therefrom the attenuation coefficients of the remaining sub-carriers at using an interpolation in the frequency domain.

Channel estimation in FBMC telecommunication systems uses similar techniques. You will find in the article of E. Kofidis et al. entitled “Preamble-based channel estimation in OFDM/OQAM systems: a review”, May 8, 2013 , a review of different channel estimation methods in systems using FBMC modulation.

However, the insertion of pilot symbols cannot be performed as in OFDM insofar as the time and frequency multiplexing in an FBMC frame does not guarantee the orthogonality of the components in phase and in quadrature (i.e. say of the real and imaginary parts of the received pilot symbols).

The table below gives the impulse response of an FBMC channel for an example of a prototype filter and an overlap factor K = 4. We denote by n the temporal index and k the index of the sub-carrier. k / n n -2 n -1 not n +1 n +2 k -1 -0.125 -0.206d 0.239 0.206d -0.125 k 0 0.564 1 0.564 0 k +1 -0.125 0.206d 0.239 -0.206d -0.125

It is thus understood that a symbol at time n and on carrier k can generate interference in a neighborhood in time and frequency around the position ( n , k ), this interference being real or imaginary depending on the position considered within this neighborhood.

Thus if a pilot symbol +1 is transmitted in position ( n , k ) and an imaginary datum αj is transmitted in position ( n, k -1), the following symbols are received: k / n n -2 n -1 not n +1 n +2 k-1 -0.125 0.564α - 0.206j 0.239+αj 0.564α + 0.206j -0.125 k -0.125 aj 0.564 + 0.206d 1+0.239αj 0.564 - 0.206d -0.125αj k +1 -0.125 0.206d 0.239 -0.206d -0.125

, il n'en va pas de même pour la partie imaginaire de ce coefficient. Inversement si la donnée adjacente au symbole pilote avait été réelle, on n'aurait pu estimer la partie imaginaire du coefficient de canal de transmission, $h_k^I$

, mais non sa partie réelle.We understand in this example that if we can recover the real part of the transmission channel coefficient, $h_k^R$

, it is not the same for the imaginary part of this coefficient. Conversely, if the data adjacent to the pilot symbol had been real, it would not have been possible to estimate the imaginary part of the transmission channel coefficient, $h_k^I$

, but not its real part.

To remedy this difficulty, it has been proposed in particular to calculate the surrounding data so as to cancel the interference affecting the pilot symbol on reception (cf. article by E. Kofidis cited above). However, this introduces complexity on the transmitter side (complex calculation of the preamble) and increases the latency of the system. Furthermore, this pre-emphasis can lead locally to high levels of PAPR ( Peak-to-Average Power Ratio ) and therefore to amplifier saturation problems.

Whatever the implementation, temporal or frequency, of the receiver, the equalization is generally carried out in the frequency domain, after the filtering by the prototype filter (that is to say at the output of the FFT module 170 of the Fig. 1 or module 270 of the Fig. 2 ). The aforementioned article by Bellanger proposes alternatively to carry it out, in the frequency domain, before filtering by the prototype filter (that is to say between the FFT module 260 and the filter 270 of the Fig. 2 ). However, this document does not specify how to perform the channel estimation then. Indeed, at this stage, the impulse response of the system is modified due to the absence of filtering by the prototype filter and the channel estimation is not trivial. The article " OFDM and FMBC transmission techniques: a compatible high performance proposal for broadband power line communications" by M Bellanger, ISPLC 2010 , teaches a method that uses a weighting function to reduce edge effects.

The object of the present invention is to propose a channel estimation method in an FBMC telecommunication system, which does not have the aforementioned drawbacks, in particular which does not require pre-emphasis at the transmitter level and which is simple to implement. implemented.

DISCLOSURE OF THE INVENTION

• on effectue une FFT sur le signal reçu par le récepteur, avant que celui-ci ne soit filtré par le banc de filtres d'analyse;
• on extrait des blocs de composantes en sortie de la FFT les symboles pilotes reçus pendant tout ou partie du préambule ;
• on effectue une estimation des coefficients du canal pour ladite pluralité de sous-porteuses en combinant pour chaque sous-porteuse les composantes relatives à cette sous-porteuse et à des blocs successifs au moyen d'une pluralité de coefficients de pondération prédéterminés.

The present invention is defined by the methods of claims 1 and 4. Further embodiments are subject of the dependent claims. In general terms, the invention relates to a channel estimation method for an FBMC telecommunication system comprising a transmitter and a receiver, the transmitter being equipped with a bank of synthesis filters and the receiver being equipped with a bank of analysis filters, the analysis and synthesis filters being frequency shifted versions of a prototype filter, the signal transmitted by the transmitter comprising a preamble followed by data symbols, the preamble comprising pilot symbols distributed in time and frequency, over a plurality of subcarriers, wherein:

• an FFT is performed on the signal received by the receiver, before the latter is filtered by the bank of analysis filters;
• the pilot symbols received during all or part of the preamble are extracted from the blocks of components at the output of the FFT;
• the coefficients of the channel are estimated for said plurality of sub-carriers by combining, for each sub-carrier, the components relating to this sub-carrier and to successive blocks by means of a plurality of predetermined weighting coefficients.

The specific features of the claimed solution are disclosed below.

The preamble advantageously consists of a repetition over time of the same pilot symbols distributed over said plurality of sub-carriers

The pilot symbols may in particular all be identical.

Preferably, it is provided that at each instant of transmission, a sub-carrier on Q consecutive subcarriers carries a pilot symbol, Q being an integer greater than or equal to 2, the other subcarriers carrying a zero symbol.

, où v est le nombre de blocs successifs pris en considération pour l'estimation du coefficient de canal relatif à la sous-porteuse, σ_k dépendant de la réponse impulsionnelle du filtre prototype ainsi que des symboles pilotes présents dans le support temporel et fréquentiel de ce filtre.According to a first embodiment, the channel estimation is performed only on the stationary part of the preamble, the weighting coefficients relating to the same sub-carrier and to successive blocks, are identical and equal to $\frac{1}{{\mathit{\nu \sigma }}_k}$

, where v is the number of successive blocks taken into consideration for the estimation of the channel coefficient relative to the sub-carrier, σ _k depending on the impulse response of the prototype filter as well as on the pilot symbols present in the time and frequency medium of this filter.

According to a second embodiment, the weighting coefficients ( µ _{n , k} ) relating to the same sub-carrier and to different blocks are a function of the impulse response of the prototype filter, of the size of the preamble, of the pilot symbols present in the time and frequency support of the prototype filter and the type of data used in the frame.

The channel estimate relating to a sub-carrier is advantageously obtained as an MRC combination of estimates made from the successive blocks obtained over the entire duration of the preamble.

Said weighting coefficients can be calculated iteratively, the channel coefficients estimated from the weighting coefficients obtained during an iteration being used to estimate the data following the preamble, during the following iteration and, conversely, the data thus estimated during an iteration being used to update said weighting coefficients at the following iteration.

It is possible to perform an interpolation in the frequency domain between the coefficients of the channel to obtain a channel coefficient relating to a sub-carrier not carrying a pilot symbol.

The invention also relates to an equalization method within an FBMC receiver, in which a channel estimation is carried out as indicated above, from the pilot symbols distributed in time and frequency within the preamble and in which a ZF or MMSE type equalization is carried out on the data symbols following the preamble, by means of the channel coefficients estimated for the said plurality of sub-carriers.

BRIEF DESCRIPTION OF DRAWINGS

• La Fig. 1 représente une première implémentation d'un système de télécommunication FBMC connu de l'état de la technique ;
• La Fig. 2 représente une seconde implémentation d'un système de télécommunication FBMC connu de l'état de la technique ;
• La Fig. 3A illustre l'étalement spectral réalisé en amont du module IFFT de la Fig. 2 ;
• La Fig. 3B illustre le désétalement spectral réalisé en aval du module FFT dans la Fig. 2 ;
• La Fig. 4 illustre la combinaison des symboles FBMC dans la Fig. 2 ;
• La Fig. 5 illustre un exemple de signal en sortie d'un émetteur FBMC, avant conversion RF ;
• La Fig. 6 représente schématiquement un exemple de récepteur FBMC mettant en œuvre une méthode d'estimation de canal selon un mode de réalisation de l'invention.

Other characteristics and advantages of the invention will appear on reading preferred embodiments of the invention made with reference to the attached figures, including:

• The Fig. 1 represents a first implementation of an FBMC telecommunication system known from the state of the art;
• The Fig. 2 represents a second implementation of an FBMC telecommunication system known from the state of the art;
• The Fig. 3A illustrates the spectral spreading carried out upstream of the IFFT module of the Fig. 2 ;
• The Fig. 3B illustrates the spectral despreading carried out downstream of the FFT module in the Fig. 2 ;
• The Fig. 4 illustrates the combination of FBMC symbols in the Fig. 2 ;
• The Fig. 5 illustrates an example of an output signal from an FBMC transmitter, before RF conversion;
• The Fig. 6 schematically represents an example of an FBMC receiver implementing a channel estimation method according to an embodiment of the invention.

DETAILED DISCUSSION OF PARTICULAR EMBODIMENTS

We will consider below an FBMC telecommunication system comprising at least one transmitter and one receiver. For example, the transmitter can be a base station and the receiver a terminal (downlink) or the transmitter can be a terminal and the receiver a base station (uplink).

The signal transmitted by the transmitter comprises a preamble consisting of pilot symbols, followed by data symbols. The pilot symbols and the data symbols are subject to FBMC modulation as described in the introduction.

The basic idea of the invention is to perform the equalization upstream of the filtering by the prototype filter, by choosing an appropriate form of preamble and by combining for each subcarrier channel estimates obtained at instants of successive reception within the preamble.

The Fig. 5 represents the form of a preamble transmitted by an FBMC transmitter, before transposition into the RF band.

In this example, it has been assumed that one sub-carrier out of two is transmitted with a pilot symbol, the other sub-carriers being assigned null symbols. For the same sub-carrier, the successive pilot symbols within the preamble are identical. Thus, in the present case, one out of two sub-carriers carries the sequence of pilot symbols +1,+1,...,+1 and the other sub-carriers carry zero sequences, this for the entire duration of the preamble.

Three distinct zones can be distinguished in the waveform of the preamble: a first zone, 510, at the start of the preamble, corresponding to a transient state of duration substantially equal to the rise time of the prototype filter, a second zone, 520, corresponding to a steady state, in which the envelope of the signal is substantially constant, and a third zone, 530, at the end of the preamble, again corresponding to a transient state, of duration substantially equal to the fall time of the prototype filter.

The preamble waveform in the first transient region is generally not symmetrical to that in the second transient region. Indeed, during the second transient zone, the data following the preamble influence the waveform due to the time overlap of the prototype filters.

les symboles pilotes P ₀,...,P _N-1 étant respectivement portés par les N sous porteuses. En définitive, le préambule peut être représenté par le tableau suivant dans lequel, comme précédemment, les lignes correspondent aux sous-porteuses et les colonnes aux instants de transmission : P ₀ P ₀ P ₀ P ₀ ... P ₀ P ₀ P ₁ P ₁ P ₁ P ₁ ... P ₁ P ₁ P ₂ P ₂ P ₂ P ₂ ... P ₂ P ₂ ⋮ ⋮ ⋮ ⋮ ... ⋮ ⋮ P _N-1 P _N-1 P _N-1 P _N-1 ... P _N-1 P _N-1 In a first embodiment, it is assumed that a repeating pattern of pilot symbols is transmitted throughout the duration of the preamble. In other words, at each transmission instant n of the preamble, the transmitter transmits the block of symbols: $$x_0\left[\mathrm{not}\right]={\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0005.png"\; state="\{\{state\}\}">P</figure-callout>}}_0;x_1\left[\mathrm{not}\right]={\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_1;\dots ;x_{\mathrm{NOT}-1}\left[\mathrm{not}\right]=P_{\mathrm{NOT}-1}$$

the pilot symbols P ₀ ,..., P _{N -1} being respectively carried by the N sub-carriers. Ultimately, the preamble can be represented by the following table in which, as previously, the rows correspond to the sub-carriers and the columns to the instants of transmission: P0 _{_} P0 _{_} P0 _{_} P0 _{_} ... P0 _{_} P0 _{_} P1 _{_} P1 _{_} P1 _{_} P1 _{_} ... P1 _{_} P1 _{_} P2 _{_} P2 _{_} P2 _{_} P2 _{_} ... P2 _{_} P2 _{_} ⋮ ⋮ ⋮ ⋮ ... ⋮ ⋮ P _{N -1} P _{N -1} P _{N -1} P _{N -1} ... P _{N -1} P _{N -1}

In an advantageous embodiment variant, provision may be made for one out of two sub-carriers to carry a pilot symbol (for example the sub-carriers of even indices) and for the other sub-carriers to carry zero symbols. This variant can be declined in a more general way, by providing that a sub-carrier on Q ( Q integer greater than or equal to 2) consecutive sub-carriers will carry a pilot symbol, the other sub-carriers carrying a zero symbol.

Whatever the variant, the pilot symbols may be identical. Thus in the case of a pilot symbol/zero symbol alternation, the preamble will have the following structure: P P P P ... P P 0 0 0 0 ... 0 0 P P P P ... P P 0 0 0 0 ... 0 0 ⋮ ⋮ ⋮ ⋮ ... ⋮ ⋮ P P P P ... P P

In the first embodiment, the channel estimation is performed from the pilot symbols of the preamble in the steady state zone, i.e. after the rise time of the prototype filter, the rise of the filter starting at the beginning of the preamble and before the fall time of the prototype filter, the fall of the filter ending at the end of the preamble.

It is assumed that the channel response does not vary during the duration of the preamble.

dans lequel on a respectivement noté I_t et I_f le support temporel et le support fréquentiel de la réponse impulsionnelle du filtre prototype, n est l'indice du bloc temporel et k est l'indice de la sous-porteuse.In this case, the FBMC signal at the channel output, after translation into baseband and sampling but before filtering by the bank of analysis filters, can be written, in steady state: $$r\left(\mathrm{not}\right)={\displaystyle \sum _k{h}_k\left({\displaystyle \sum _{p;\mathrm{not}-p\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_I{g}_{\mathrm{not}-p,k-I}}}\right)}$$

in which I _t and I _f respectively denote the temporal support and the frequency support of the impulse response of the prototype filter, n is the index of the temporal block and k is the index of the sub-carrier.

It follows from (4) that in steady state, the symbol r _k ( n ) received on a sub-carrier k is theoretically constant and equal to: $$r_k\left(\mathrm{not}\right)=h_k\left({\displaystyle \sum _{p\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_I{g}_{q,k-I}}}\right)=r_k$$

The term in parentheses is known to the receiver since the pilot symbols are by definition known and the coefficients of the prototype filter are also known.

In practice, the symbols transmitted on the various sub-carriers are not only affected by an attenuation coefficient (complex coefficient) but also by a noise which we will assume Gaussian additive white.

où v est le nombre de symboles pris en considération dans le régime stationnaire.The channel estimate for subcarrier k is then given by: $$〈h_k〉=\frac{1}{\nu \left({\displaystyle \sum _{q\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_I{g}_{q,k-I}}}\right)}{\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\nu }{r}_k\left(\mathrm{not}\right)}$$

where v is the number of symbols considered in the steady state.

où les ${\sigma }_k=\left({\displaystyle \sum _{q\in I_t}{\displaystyle \sum _{i;k-i\in I_{ƒ}}{P}_i{g}_{q,k-i}}}\right)$

, k = 0,...,N -1 sont les sommes (complexes) ainsi pré-calculées.It will be noted that the sum in the denominator of the expression (6) can be calculated once and for all from the pilot symbols P ₀ ,..., P _{N -1} and the response of the prototype filter, this for each sub- carrier. Expression (6) can then be rewritten: $$〈h_k〉=\frac{1}{{\mathit{\nu \sigma }}_k}{\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\nu }{r}_k\left(\mathrm{not}\right)}$$

where the ${\sigma }_k=\left({\displaystyle \sum _{q\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_I{g}_{q,k-I}}}\right)$

, k = 0,..., N -1 are the (complex) sums thus pre-computed.

The first embodiment however assumes that the preamble is long enough for a steady state to be established. More precisely, for a prototype filter of duration KN, the preamble must be of duration at least equal to (2 K -1) N. This preamble duration can be penalizing when the data frames are short (high overhead/data ratio) . In this case, it will be preferred to implement the second embodiment of the invention.

In the second embodiment, it is assumed that a preamble composed of a predetermined pattern of pilot symbols is transmitted. The pattern may consist of the temporal repetition of an elementary pattern as in the first embodiment. However, unlike the first embodiment, the constancy constraint over time can be relaxed, in other words it is not necessary for the pilot symbols carried by the same sub-carrier to be identical.

où P _p,i est le symbole pilote porté par la sous-porteuse d'indice p à d'instant de transmission i.In this case, the signal at the output of the transmission channel, after translation into baseband, can be written: $$r\left(\mathrm{not}\right)={\displaystyle \sum _k{h}_k\left({\displaystyle \sum _{p;\mathrm{not}-p\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_{g,I}{g}_{\mathrm{not}-p,k-I}}}\right)}$$

where P _{p , i} is the pilot symbol carried by the subcarrier of index p at instant of transmission i .

For each pilot symbol P _{n , k ,} the signal-to-interference ratio at the receiver can be estimated by: $${\lambda }_{\mathrm{not},k}=\frac{{\left|P_{\mathrm{not},\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">k</figure-callout>}}\right|}^2}{{\left|{\displaystyle \sum _{\begin{array}{l}p\ne \mathrm{not}\\ \mathrm{not}-p\in I_{\mathrm{you}}\end{array}}{\displaystyle \sum _{\begin{array}{l}I\ne k\\ k-I\in I_{ƒ}\end{array}}{P}_{p,I}{g}_{\mathrm{not}-p,k-I}}}\right|}^2}$$

où v est le nombre d'instants de réception considérés dans le préambule.The channel estimate for the sub-carrier k is then obtained by performing an MRC ( Maximum Ratio Combining ) combination of the estimates at different times of reception of the preamble, i.e.: $$〈h_k〉=\frac{1}{{\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\bar{\nu }}{\lambda }_{\mathrm{not},k}}}{\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\bar{\nu }}{\lambda }_{\mathrm{not},k}\frac{r_k\left(\mathrm{not}\right)}{\left({\displaystyle \sum _{p;\mathrm{not}-p\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_{g,I}{g}_{\mathrm{not}-p,k-I}}}\right)}}$$

where v is the number of reception instants considered in the preamble.

The instants of reception considered can here be chosen outside the steady state, in particular during the first transient zone 510 or during the second transient zone 530 of the Fig. 5 . However, if samples are taken account in the second transitory zone, data symbols appear in the sum in the denominator of the expression (9) as well as in that in the denominator of the expression (10), due to the overflow of the support of the prototype filter on the part "data" of the frame. Statistical processing is then used by averaging over the various possible data symbols. It can be assumed for this purpose that the probability density of the OQAM symbols is evenly distributed.

When the considered reception instants are taken in the first transient state zone or the stationary state zone, the (complex) weighting coefficients involved in the expression (10) can be calculated once and for all and stored in a table of receiver, either: $${\mu }_{\mathrm{not},k}=\frac{{\lambda }_{\mathrm{not},k}}{{\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\bar{\nu }}{\lambda }_{\mathrm{not},\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}}}\frac{1}{\left({\displaystyle \sum _{p;\mathrm{not}-p\in I_{\mathrm{you}}}{\displaystyle \sum _{I;k-I\in I_{ƒ}}{P}_{p,I}{g}_{\mathrm{not}-p,k-I}}}\right)}$$

Expression (10) then reduces more simply to: $$〈h_k〉={\displaystyle \sum _{\mathrm{not}={\mathrm{not}}_0}^{{\mathrm{not}}_0+\nu }{\mu }_{\mathrm{not},k}{r}_k\left(\mathrm{not}\right)}$$

When certain instants of reception, taken into account for the channel estimation, are located in the second transitory zone of the preamble, it is still possible to pre-calculate the coefficients µ _{n , k} but, this time, by carrying out a statistical average on the data symbols involved in the sum in the denominator of the expression (9) and in that in the denominator of the expression (11). More precisely when a symbol P _{p , i} appearing in this sum is in fact a data symbol, the various possible OQAM symbols are considered with the same probability and the mean value of μ _{n , k} is calculated.

More generally, it will be possible to determine, by simulation, the weighting coefficients µ _{n , k} taking into account the type of prototype filter, the rise time (equal to the fall time) of the prototype filter, the size of the preamble, the type of data used in the frame. The weighting coefficients are then stored in a table ( look-up table ) of the receiver which is addressed by the aforementioned parameters.

According to a variant of the second embodiment, it is possible to perform an iterative estimation of the channel. During the first iteration, a first estimate of the coefficients is obtained from the MRC weighting coefficients as explained above. During each of the successive iterations, these weighting coefficients are then updated by estimating the data following the preamble, after these data have been equalized by means of the channel coefficients estimated at the previous iteration. Thus, as the iterations progress, the channel estimation makes it possible to refine the estimation of these data and therefore the weighting coefficients. Conversely, the more precise estimation of the data makes it possible to update the weighting coefficients and to refine the channel estimation. The iterations can be stopped when a convergence criterion is satisfied or after a predetermined number of iterations.

The Fig. 6 illustrates an example of an FBMC receiver implementing a channel estimation method according to one embodiment of the invention.

The FBMC receiver shown uses a frequency implementation as shown in Fig. 2 .

The received signal is translated into baseband and sampled at the rate Nf and subjected to an FFT of size KN, in the FFT module, 610.

For each block of samples output from the FFT, the extraction module, 620, extracts the received pilot symbols.

In the first embodiment, the extraction of the pilot symbols takes place during the stationary regime of the preamble, in the second embodiment, it can take place during all or part of the preamble, independently of the stationary or transient nature of the part considered.

The channel estimation module, 630, performs channel estimation using expression (7) or (12), depending on the embodiment considered.

The complex coefficients σ _k or μ _{n , k} are stored in a memory 635. If necessary, this memory can be addressed by parameters (filter length, preamble size, etc.) as explained above.

The channel coefficient estimates 〈 h _k 〉 for each subcarrier k carrying a pilot symbol are supplied to the interpolation module 640. This module determines the missing channel coefficients by interpolation. Thus, when the channel coefficient is estimated only for a subcarrier on Q , it will be possible to proceed by interpolation to an estimation of channel coefficients for the remaining subcarriers.

, k = 0,...,N -1, alors qu'une égalisation de type MMSE consister à multiplier ces mêmes symboles par les coefficients $\frac{h_k^{\ast }}{{\left|h_k\right|}^2+{\sigma }^2}$

, k = 0,...,N -1 où σ ² est une estimation de la puissance de bruit sur chaque sous-porteuse (la puissance de bruit est supposée identique sur les différentes sous-porteuse).The channel coefficients for all the sub-carriers are then supplied to the equalization module 650. This module performs a ZF or MMSE equalization of the symbols received from the channel coefficients thus estimated. It is recalled that a ZF type equalization consists in multiplying the symbols on the different sub-carriers by the coefficients $\frac{1}{h_k}$

, k = 0,..., N -1, whereas an MMSE type equalization consists in multiplying these same symbols by the coefficients $\frac{h_k^{\ast }}{{\left|{\mathrm{<figure-callout\; id="2"\; label="h\; k"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">h</figure-callout>}}_k\right|}^2+{\mathrm{<figure-callout\; id="2"\; label="\sigma "\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}^2}$

, k = 0,..., N -1 where σ ² is an estimate of the noise power on each subcarrier (the noise power is assumed to be identical on the different subcarriers).

After equalization, the symbols are filtered in the frequency domain by an analysis filter bank (frequency-translated copies of the prototype filter), 660, then supplied to an OQAM demodulation module.

The channel estimation method according to the first or the second embodiment of the invention can also be applied in the case of a time-based implementation of the FBMC receiver. In this case, the equalization is carried out in the time domain downstream of the filtering by the bank of analysis filters.

Claims (7)

1. Channel estimating method for an FBMC telecommunication system comprising a transmitter and a receiver, the transmitter being provided with a synthesis filter bank and the receiver being provided with an analysis filter bank, the analysis and synthesis filters being frequency shifted versions of a prototype filter, the signal transmitted by the transmitter comprising a preamble followed by data symbols, the preamble comprising pilot symbols distributed in time and in frequency, on a plurality N of sub-carriers, characterised in that the preamble is composed of a repetition in time of the same pilot symbols distributed on said plurality of sub-carriers, the preamble being of duration greater than or equal to (2K -1)N in which K is the overlapping factor of the prototype filters, and in that:

   - an FFT is done on the signal received by the receiver, before the signal is filtered by the analysis filter bank;

   - the pilot symbols received during all or some of the preamble are extracted from the frequency component blocks output from the FFT;

   - channel coefficients are estimated for said plurality of sub-carriers by taking each sub-carrier and combining the components for this sub-carrier and for successive blocks and by weighting the combination obtained by a weighting factor associated with a sub-carrier, said estimate only being made on the stationary part of the preamble, the weighting factor for one sub-carrier and successive blocks, being equal to $\frac{1}{{\mathit{\nu \sigma }}_k}$

   

   , where v is the number of successive blocks considered to estimate the channel coefficient for the sub-carrier, and ${\sigma }_k=\left({\displaystyle \sum _{q\in I_t}{\displaystyle \sum _{i;k-i\in I_{ƒ}}{P}_i{g}_{q,k-i}}}\right)$

   

   in which g_q,k, q ∈ I_t are the coefficients of the prototype filter associated with the subcarrier k and P_i are the pilot symbols present in the temporal support I_t and frequency support I_f of this filter.
2. Channel estimating method according to claim 1, characterised in that the pilot symbols are all identical.
3. Channel estimating method according to claim 2, characterised in that at each transmission instant, one sub-carrier out of Q consecutive sub-carriers carries a pilot symbol, where Q is an integer greater than or equal to 2, the other sub-carriers carrying a null symbol.
4. Channel estimating method for an FBMC telecommunication system comprising a transmitter and a receiver, the transmitter being provided with a synthesis filter bank and the receiver being provided with an analysis filter bank, the analysis and synthesis filters being frequency shifted versions of a prototype filter, the signal transmitted by the transmitter comprising a preamble followed by data symbols, the preamble comprising pilot symbols distributed in time and in frequency, on a plurality N of sub-carriers, characterised in that:

   - an FFT is done on the signal received by the receiver, before the signal is filtered by the analysis filter bank;

   - the pilot symbols received during all or some of the preamble are extracted from the frequency component blocks output from the FFT;

   - channel coefficients are estimated for said plurality of sub-carriers by taking each sub-carrier and combining the components for this sub-carrier and for successive blocks by means of a plurality of a weighting factors, the weighting factors (µ _n,k ) for a same sub-carrier k and for different blocks n = n ₀,..,n ₀ + v, in which n ₀,..,n ₀ + v are reception instants in a stationary condition zone of the preamble, and in which said weighting factors are equal to ${\mu }_{n,k}=\frac{{\lambda }_{n,k}}{{\displaystyle \sum _{n=n_0}^{n_0+\bar{\nu }}{\lambda }_{n,k}}}\frac{1}{\left({\displaystyle \sum _{p;n-p\in I_t}{\displaystyle \sum _{i;k-i\in I_{ƒ}}{P}_{p,i}{g}_{n-p,k-i}}}\right)}$

   

   in which λ _n,k is an estimate of the signal-to-interference ratio at the receiver based on the pilot symbol P_n,k and g _{q, k}, q ∈ I_t are coefficients of the prototype filter associated with the subcarrier k ; I_t and I_f being respectively the temporal support and the frequency support of this filter.
5. Channel estimating method according to one of claims 4, characterised in that said weighting factors are calculated iteratively, the channel coefficients estimated from weighting factors obtained during one iteration are used to estimate the data following the preamble, during the next iteration, and vice versa, the data thus estimated during one iteration being used to update said weighting factors during the next iteration.
6. Channel estimating method according to one of the previous claims, characterised in that interpolation is done in the frequency domain between channel coefficients to obtain a channel coefficient for a sub-carrier not carrying a pilot symbol.
7. Equalisation method within an FBMC receiver, characterised in that a channel estimate is made according to one of the previous claims, using pilot symbols distributed in time and in frequency within the preamble and in that a ZF or MMSE type equalisation is made on the data symbols following the preamble, making use of the channel coefficients estimated for said plurality of sub-carriers.

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